January 22, 2021

About the presenter

Three main componenets of Bayesian inference

  • Likelihood
  • Prior distribution
  • Posterior distribution

True data-generating mechanism

Formula for Posterior model probability and Bayes factor

  • Posterior model probability

\[ p(\mathcal{M}_{i}|data) = \frac{ p(data|\mathcal{M}_{i}) p(\mathcal{M}_{i}) } { \sum_{j=1}^{n}p(data|{\mathcal{M}}_{j})p(\mathcal{M}_{j}) } \]

  • Bayes factor

\[ \frac{p(\mathcal{M}_{1}|data)}{p(\mathcal{M}_{2}|data)} = \frac {\frac{p(data|\mathcal{M}_{1})p(\mathcal{M}_{1})} {\sum_{j=1}^{n}p(data|{\mathcal{M}}_{j})p(\mathcal{M}_{j})}} {\frac{p(data|\mathcal{M}_{2})p(\mathcal{M}_{2})} {\sum_{j=1}^{n}p(data|{\mathcal{M}}_{j})p(\mathcal{M}_{j})}} = \frac{p(data|\mathcal{M}_{1})}{p(data|\mathcal{M}_{2})} \times \frac{p(\mathcal{M}_{1})}{p(\mathcal{M}_{2})} \]

Prior distributions

Tables

datatable(PoliticalDemocracy, options = list(pageLength = 6))

Citation

See Heo and Schoot (2020a); Heo and Schoot (2020b) for tutorials.

Heo, Ihnwhi, and Rens van de Schoot. 2020a. “Advanced Bayesian Regression in JASP.”

———. 2020b. “JASP for Bayesian Analyses with Informative Priors (Using JAGS).”